EP3633411A1 - Procédé d'estimation d'image de coefficient d'absorption, programme d'estimation d'image de coefficient d'absorption et dispositif de tomographie par positrons équipé de ce dernier - Google Patents

Procédé d'estimation d'image de coefficient d'absorption, programme d'estimation d'image de coefficient d'absorption et dispositif de tomographie par positrons équipé de ce dernier Download PDF

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EP3633411A1
EP3633411A1 EP17912063.9A EP17912063A EP3633411A1 EP 3633411 A1 EP3633411 A1 EP 3633411A1 EP 17912063 A EP17912063 A EP 17912063A EP 3633411 A1 EP3633411 A1 EP 3633411A1
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Prior art keywords
image
attenuation coefficient
value
projection data
coefficient
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German (de)
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EP3633411A4 (fr
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Tetsuya Kobayashi
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Shimadzu Corp
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Shimadzu Corp
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T11/00—2D [Two Dimensional] image generation
    • G06T11/003—Reconstruction from projections, e.g. tomography
    • G06T11/008—Specific post-processing after tomographic reconstruction, e.g. voxelisation, metal artifact correction
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B6/00—Apparatus or devices for radiation diagnosis; Apparatus or devices for radiation diagnosis combined with radiation therapy equipment
    • A61B6/52—Devices using data or image processing specially adapted for radiation diagnosis
    • A61B6/5211—Devices using data or image processing specially adapted for radiation diagnosis involving processing of medical diagnostic data
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T11/00—2D [Two Dimensional] image generation
    • G06T11/003—Reconstruction from projections, e.g. tomography
    • G06T11/006—Inverse problem, transformation from projection-space into object-space, e.g. transform methods, back-projection, algebraic methods
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/0002—Inspection of images, e.g. flaw detection
    • G06T7/0012—Biomedical image inspection
    • G06T7/0014—Biomedical image inspection using an image reference approach
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/10—Image acquisition modality
    • G06T2207/10072—Tomographic images
    • G06T2207/10104—Positron emission tomography [PET]

Definitions

  • the present invention relates to an attenuation coefficient image estimation method, an attenuation coefficient image estimation program, a positron CT apparatus equipped with the same, which estimate an attenuation coefficient image from measurement data of a positron CT apparatus (positron emission tomography).
  • a positron CT apparatus i.e., a PET (Positron Emission Tomography) apparatus, is configured to measure two ⁇ -rays generated by positron annihilation regarded as valid signals only when they are simultaneously detected by a plurality of detectors (that is, only when they are coincidentally counted), and the tomographic image of the subject is reconstructed based on the measurement data.
  • a radioactive pharmaceutical containing positron emitting nuclides is administered to a subject, the 511 keV annihilation ⁇ -rays emitted from the administered subject are detected by detectors composed of a number of detector elements (e.g., scintillators).
  • ⁇ -rays when ⁇ -rays are detected within a fixed time period with two detectors, it is regarded as being detected "coincidentally", they are counted as a pair of annihilation ⁇ -rays, and furthermore, a straight line (LOR: Line Of Response) connecting two detectors that detected the annihilation occurrence positions is specified.
  • LOR Line Of Response
  • positron CT In order to perform a quantitative measurement of a radioactivity concentration in a subject, various data correction processing are required. Representative correction processing include sensitivity correction, scatter correction, random correction, decay correction, dead time correction, and attenuation correction,.
  • the present invention relates to an attenuation correction for preventing a decrease in image quantitative performance due to the attenuation of ⁇ -rays emitted from a radioactive pharmaceutical (radioisotope).
  • radioactive pharmaceutical radioactive pharmaceutical
  • the transmittance of ⁇ -rays is obtained from the estimated attenuation coefficient image, and the measurement data of PET is divided by the transmittance to convert into data from which the influence of the attenuation of ⁇ -rays has been eliminated.
  • the estimated attenuation coefficient image is incorporated into the calculation formula of the image reconstruction to obtain a reconstructed image from which the influence of the attenuation of ⁇ -rays has been eliminated.
  • transmission data obtained by irradiating the positron-emitting nuclide with the external radiation source is needed.
  • CT data obtained from an X-ray CT (Computed Tomography) apparatus instead of transmission data.
  • non-Patent Documents 1 and 2 there is a reconstruction algorithm that does not require such transmission data (see, for example, non-Patent Documents 1 and 2).
  • TOF-PET detection time difference
  • the radioactivity image and the attenuation coefficient sinogram can be estimated simultaneously.
  • the reconstruction algorithm in non-Patent Documents 1 and 2 is also called “simultaneous reconstruction algorithm" because it simultaneously estimates the radioactivity image and the data regarding attenuation coefficient (for example, attenuation coefficient sinogram).
  • the simultaneous reconstruction algorithm that simultaneously estimates the radioactivity image and the attenuation coefficient sinogram is referred to as an MLACF method.
  • the principle of the MLACF method will be described qualitatively with reference to the conceptual diagram of FIG. 9 . It is assumed that the radioactivity concentration is distributed as shown in FIG. 9 in the target region of the subject.
  • the radioactivity distribution is projected to a two-dimensional distribution of the TOF information t and the radial direction s, when the projection direction ⁇ is 0°, it becomes as shown in the upper view of FIG. 9 , and when the projection direction ⁇ is 90°, it becomes as shown in the right view of FIG. 9 .
  • the projection direction ⁇ is in the range of 0° to 180°, a two-dimensional distribution for each projection angle ⁇ is obtained as measurement data.
  • the attenuation coefficient sinogram in which the attenuation coefficient value is converted into a sinogram format can be estimated simultaneously with the radioactivity image using the measurement data of the TOF information.
  • the following technology is indispensable. That is, a technique for estimating an attenuation coefficient image in which the absolute value is correct from an attenuation coefficient sinogram in which the distribution shape is correct but the absolute value is incorrect.
  • non-Patent Document 2 there is a method of directly quantifying a radioactivity image without directly quantifying an attenuation coefficient sinogram.
  • the processing step is as follows.
  • Non-Patent Document 2 described above, there is a problem that it cannot be guaranteed in principle that the finally obtained radioactivity image is quantitative.
  • the present invention has been made in view of the above-described circumstances, and aims to provide an attenuation coefficient image estimation method, an attenuation coefficient image estimation program, and a positron CT apparatus equipped with the same, which are capable of generating a quantitative attenuation coefficient image.
  • the inventor has obtained the following findings as a result of earnest studies to solve the above problems.
  • the present invention based on such findings has the following configuration.
  • an attenuation coefficient image estimation method is an attenuation coefficient image estimation method of estimating an attenuation coefficient image from measurement data of a positron CT including time-of-flight information of annihilation radiation.
  • the method includes:
  • the reconstruction calculation step based on the optimization of the evaluation function regarding the measurement data (measurement data of TOF-PET) of the positron CT in which the time-of-flight information of the annihilation radiation is included, an image in which the non-uniform offset value is added to the quantitative attenuation coefficient image is calculated.
  • ⁇ ' is a non-quantitative radioactivity image
  • the radioactivity image ⁇ ' is calculated in the reconstruction calculation step.
  • the reconstruction algorithm in the reconstruction calculation step here is the simultaneous reconstruction algorithm described above.
  • subject mask projection data in the projection data space (hereinafter referred to as "subject mask projection data") is calculated based on the measurement data.
  • ⁇ off is a non-uniform offset image
  • an offset image ⁇ off is estimated by the reconstruction algorithm configured such that the forward projection data of the offset image ⁇ off approximates the subject mask projection data.
  • ⁇ is a region that can be approximated by a known attenuation coefficient value
  • the reference region extraction step at least one region ⁇ is extracted.
  • the "an image in which the subject region is recognizable calculated based on measurement data” is, for example, the image ⁇ ' mentioned above, the radioactivity image ⁇ ' mentioned above, the non-quantitative image estimated by the reconstruction algorithm different from the reconstruction algorithm (simultaneous reconstruction algorithm) in the reconstruction calculation step mentioned above, and the subject mask image estimated from the subject mask projection data mentioned above.
  • the image is not limited to the exemplified images, and may be any image in which the subject region is recognizable calculated based on the measurement data.
  • extracting at least one or more regions ⁇ using an image in which a subject region is recognizable calculated based on the measurement data includes not only extracting the region ⁇ using a single piece of image information, but also extracting the region ⁇ using a combination of a plurality of pieces of image information (for example, logical sum or logical product).
  • the following coefficient calculation step and attenuation coefficient value correction step are performed using the images ⁇ ', the offset image ⁇ off , and the region ⁇ obtained in the above-described steps.
  • ⁇ is an unknown true attenuation coefficient image value (attenuation coefficient value)
  • ⁇ is a coefficient
  • the coefficient calculation step a coefficient ⁇ that reduces the error between the value of the image ⁇ ' in the region ⁇ and a known attenuation coefficient value is calculated.
  • the attenuation coefficient value correction step the value obtained by adding ⁇ off obtained by multiplying the offset image ⁇ off by the coefficient ⁇ to the value of the image ⁇ ' is corrected as an attenuation coefficient value.
  • the attenuation coefficient value is corrected in the attenuation coefficient value correction step based on the mathematical relationship in which the difference between the value of the non-quantitative image ⁇ ' in the region ⁇ and the known attenuation coefficient value (the value of the true attenuation coefficient image) can be approximated by ⁇ off obtained by multiplying the offset image ⁇ off by the coefficient ⁇ (i.e., ⁇ ⁇ ⁇ '+ ⁇ ⁇ ff ). Therefore, in the attenuation coefficient image having the attenuation coefficient value corrected in the attenuation coefficient value correction step, the systematic error becomes small. As a result, a quantitative attenuation coefficient image can be generated, which enables accurate attenuation correction of the radioactivity image.
  • the above-mentioned reconstruction calculation step may be performed by (a) a calculation algorithm in which the image ⁇ ' is included as an unknown variable.
  • the above-mentioned reconstruction calculation step may be performed by (b) a combination of a calculation algorithm in which attenuation coefficient projection data is included as an unknown variable and an algorithm in which an image obtained by reconstructing the attenuation coefficient projection data is set as the image ⁇ '.
  • the former algorithm (a) is an MLAA method that simultaneously reconstructs the non-quantitative radioactivity image ⁇ ' and the image ⁇ ' (non-quantitative attenuation coefficient image).
  • the latter algorithm (b) is a combination of the MLACF method described in non-Patent Document 1 which simultaneously estimates the non-quantitative radioactivity image ⁇ ' and the non-quantitative attenuation coefficient projection data (e.g., attenuation coefficient sinogram) and an algorithm in which the image obtained by reconstructing the attenuation coefficient projection data is set as the image ⁇ '.
  • the algorithm in which the image obtained by reconstructing the attenuation coefficient projection data is set as the image ⁇ ' in the latter (b) is not specifically limited, and may be any algorithm as long as it is a reconstruction algorithm.
  • An example of the mask calculation step mentioned above includes a step of calculating the binarized image of the image ⁇ ' as a subject mask image, a step of calculating the projection data of the subject mask image, and a step of calculating the binarized data of the projection data of the subject mask image as a subject mask projection data (Aspect (A)). Further, the mask calculation step mentioned above includes a step of calculating the projection data of the image ⁇ ' and a step of calculating the binarized data of the projection data of the image ⁇ ' as a subject mask projection data (Aspect (B)). In the above aspect (A), the projection data is calculated after binarizing the image ⁇ ' first, and the projection data is binarized.
  • the projection data of the image ⁇ ' is first calculated and then binarized.
  • the image ⁇ ' is an attenuation coefficient image that is not quantitative, but subject mask projection data can be calculated even if by binarizing the image other than the attenuation coefficient image or the projection data.
  • Another example of the mask calculation step includes the step of calculating binarized data obtained by converting the measurement data of TOF-PET described above into the projection data format and binarized it as subject mask projection data.
  • the data converted into the projection data format and binarized can be calculated as the subject projection data directly using the TOF-PET measurement data.
  • the mask calculation step includes a step of calculating a radioactivity image based on optimization of an evaluation function regarding the measurement data of (the above-described) TOF-PET, a step of calculating projection data of the radioactivity image, and a step of calculating data obtained by binarizing the projection data (of the radioactivity image) as the subject mask projection data (Aspect (C)).
  • the mask calculation step includes a step of calculating a radioactivity image based on optimization of an evaluation function regarding the measurement data of (the above-described) TOF-PET, a step of calculating a binarized image of the radioactivity image, a step of calculating projection data of the binarized image, and a step of calculating data obtained by binarizing projection data of the binarized image as the subject mask projection data (Aspect (D)).
  • the binarization is performed after the projection data of the radioactivity image is first calculated.
  • the projection data is calculated after binarizing the radioactivity image first, and the projection data is binarized.
  • the reconstruction algorithm for calculating the radioactivity image is not particularly limited.
  • subject mask projection data can be calculated utilizing the above-mentioned radioactivity image ⁇ ' estimated by the simultaneous reconstruction algorithm.
  • the subject mask projection data may be calculated utilizing a radioactivity image estimated by a reconstruction algorithm (for example, the ML-EM method) different from the above-mentioned simultaneous reconstruction algorithm (MLACF method or MLAA method).
  • the reconstruction processing performed in the above-described offset estimation step may be performed by any one of an analytical reconstruction method, a statistical reconstruction method, and an algebraic reconstruction method.
  • an analytical reconstruction method there is an FBP (Filtered Back Projection) method as the analytical reconstruction.
  • the statistical reconstruction there is, for example, the ML-EM (Maximum Likelihood-Expectation Maximization) method described above.
  • the algebraic reconstruction for example, there is the ART (Algebraic Reconstruction Technique) method.
  • At least one or more of regions ⁇ extracted in the above-described reference region extraction step is a region of a tissue in which the attenuation coefficient is regarded as known.
  • a region of a tissue in which an attenuation coefficient is regarded as known is, for example, a region that can be approximated by water, a region that can be approximated by air, a region that can be approximated by a brain tissue, a region that can be approximated by a bone, a region that can be approximated by a lung tissue, a region that can be approximated by a soft tissue, and the like.
  • the region is not limited to these illustrated tissues, but may be any tissues in which an approximation value of an attenuation coefficient can be known.
  • a brain tissue it is regarded as a region that can be approximated by water, so the attenuation coefficient value of water of 0.0096/mm can be used.
  • K ( ⁇ 1) is a number of regions that can be approximated by a known attenuation coefficient value
  • ⁇ n is an n th region ⁇
  • S(X; ⁇ n ) is a statistic of an image X in the region ⁇ n or a value calculated from the statistic as a representative value
  • T(x 1 , x 2 , ..., x K ) is any statistic of K values x 1 , x 2 , ..., x K or a value calculated from statistics of K values x 1 , x 2 , ..., x K as a representative value
  • ⁇ n is the coefficient ⁇ in the region ⁇ n .
  • the representative value is represented by, for example, a mean value, a median value, a trimmed mean value, a trimmed median value, or a weighted mean value of two or more of these values.
  • a mean value a median value, a trimmed mean value, a trimmed median value, or a weighted mean value of two or more of these values.
  • a statistic a value calculated from the statistic.
  • S( ⁇ '; ⁇ n ) is a representative value of the image ⁇ ' in the region ⁇ n
  • S( ⁇ off , ⁇ n ) is a representative value of the offset image ⁇ ⁇ ff ' in the region ⁇ n .
  • T( ⁇ 1 , ⁇ 2 , ..., ⁇ K ) is a representative value of the coefficient ⁇ 1 , ⁇ 2 , ..., ⁇ K .
  • the coefficient ⁇ can be calculated.
  • K( ⁇ 1) is a number of regions that can be approximated by a known attenuation coefficient value
  • ⁇ n is a n th region ⁇
  • D ⁇ n (X, Y) is an error evaluation function of an image X and an image Y within the region ⁇ n
  • D ⁇ n ( ⁇ n known , ⁇ '+ ⁇ off ) becomes an error evaluation function of the image ⁇ n known in which a known attenuation coefficient is set in the region ⁇ n and an image ( ⁇ ' + ⁇ off ) obtained by adding a non-uniform offset value to the quantitative attenuation coefficient image.
  • the attenuation coefficient image estimation program according to the present invention makes a computer execute the attenuation coefficient image estimation method according to the present invention.
  • the attenuation coefficient value is corrected in the attenuation coefficient value correction step based on the mathematical relationship in which the difference between the value of the non-quantitative image ⁇ ' in the region ⁇ and the known attenuation coefficient value (the value of the true attenuation coefficient image) can be approximated by ⁇ off obtained by multiplying the offset image ⁇ off by the coefficient ⁇ . Therefore, in the attenuation coefficient image having the attenuation coefficient value corrected in the attenuation coefficient value correction step, the systematic error becomes small. As a result, a quantitative attenuation coefficient image can be generated, which enables an accurate attenuation correction of the radioactivity image.
  • the positron CT apparatus is provided with a computing means for executing the attenuation coefficient image estimation program in the positron CT apparatus equipped with the attenuation coefficient image estimation program according to the present invention.
  • the computing means configured to execute the attenuation coefficient image estimation program is provided, and the attenuation coefficient value is corrected in the attenuation coefficient value correction step based on the mathematical relationship in which the difference between the value of the non-quantitative image ⁇ ' in the region ⁇ and the known attenuation coefficient value (the value of the true attenuation coefficient image) can be approximated by ⁇ off obtained by multiplying the offset image ⁇ off by the coefficient ⁇ . Therefore, in the attenuation coefficient image having the attenuation coefficient value corrected in the attenuation coefficient value correction step, the systematic error becomes small. As a result, a quantitative attenuation coefficient image can be generated, which enables an accurate attenuation correction of the radioactivity image.
  • the attenuation coefficient value is corrected in the attenuation coefficient value correction step based on the mathematical relationship in which the difference between the value of the non-quantitative image ⁇ ' in the region ⁇ and the known attenuation coefficient value (the value of the true attenuation coefficient image) can be approximated by ⁇ off obtained by multiplying the offset image ⁇ off by the coefficient ⁇ . Therefore, in the attenuation coefficient image having the attenuation coefficient value corrected in the attenuation coefficient value correction step, the systematic error becomes small. As a result, a quantitative attenuation coefficient image can be generated, which enables an accurate attenuation correction of the radioactivity image.
  • FIG. 1 is a schematic perspective view and a block diagram of a PET apparatus according to each Example
  • FIG. 2 is a schematic perspective view of a ⁇ -ray detector. Further, FIG. 1 and FIG. 2 show a configuration common to the respective Examples.
  • the PET apparatus 1 is provided with a detector ring 2 configured to surround a subject and stacked along the axial direction of the subject.
  • a plurality of ⁇ -ray detectors 3 is embedded in the detector ring 2.
  • the PET apparatus 1 corresponds to the positron CT apparatus in the present invention.
  • the ⁇ -ray detector 3 corresponds to the detector in the present invention.
  • the PET apparatus 1 is provided with a coincidence counting circuit 4 and an arithmetic circuit 5. Although only two connections from the ⁇ -ray detectors 3 to the coincidence counting circuit 4 are shown in FIG. 1 , it should be noted that connections corresponding to the total number of channels of the photomultiplier tubes (PMT: Photo Multiplier Tube) 33 (see FIG. 2 ) of the ⁇ -ray detectors 3 are connected to the coincidence counting circuit 4.
  • the arithmetic circuit 5 executes the processing of the attenuation coefficient image estimation method shown in FIG. 3 which will be described later by the attenuation coefficient image estimation program 6.
  • the arithmetic circuit 5 corresponds to the computing means in the present invention.
  • the scintillator block 31 (see FIG. 2 ) of the ⁇ -ray detector 3 converts the ⁇ -rays generated from a subject (not illustrated) to which radioactive pharmaceutical has been administered into light, and the converted light is multiplied by the photomultiplier tube (PMT) 33 (see FIG. 2 ) of the ⁇ -ray detector 3 and converted into an electric signal.
  • the electric signal is sent to the coincidence counting circuit 4 to generate detection signal data of the count value.
  • the coincidence counting circuit 4 checks the position of the scintillator block 31 (see Fig. 2 ) and the incident timing of the ⁇ -rays, and determines the sent electric signal as appropriate data only when the ⁇ -rays are simultaneously incident on two scintillator blocks 31 on both sides of the subject.
  • the coincidence counting circuit 4 rejects. That is, the coincidence counting circuit 4 detects that ⁇ -rays are simultaneously observed (that is, coincidence-counted) in two ⁇ -ray detectors 3 based on the electric signal described above.
  • the detection signal data (count value) composed of appropriate data determined to be coincidence counting by the coincidence counting circuit 4 are sent to the arithmetic circuit 5.
  • the arithmetic circuit 5 performs Steps S1 to S8 (see FIG. 3 ) which will be described later and estimates the attenuation coefficient image from the detection signal data of the subject (not illustrated) obtained by the PET apparatus 1. The specific functions of the arithmetic circuit 5 will be described later.
  • the attenuation coefficient image estimation program 6 is stored in a storage medium (not illustrated) represented by a ROM (Read-only Memory), etc.
  • the attenuation coefficient image estimation program 6 is read from the storage medium to the arithmetic circuit 5, and the attenuation coefficient image estimation program 6 is executed by the arithmetic circuit 5, thereby performing the processing of the attenuation coefficient image estimation method shown in the flowchart of FIG. 3 .
  • the arithmetic circuit 5 is configured by a programmable device (for example, an FPGA (Field Programmable Gate Array) in which the internal hardware circuit (for example, a logic circuit) can be changed according to a GPU (Graphics Processing Unit), a central processing unit (CPU), program data, and so on.
  • a programmable device for example, an FPGA (Field Programmable Gate Array) in which the internal hardware circuit (for example, a logic circuit) can be changed according to a GPU (Graphics Processing Unit), a central processing unit (CPU),
  • the ⁇ -ray detector 3 is provided with a scintillator block 31, a light guide 32 optically coupled to the scintillator block 31, and a photomultiplier tube (hereinafter simply abbreviated as "PMT") optically coupled to the light guide 33.
  • Each scintillator element constituting the scintillator block 31 converts ⁇ -rays into light by emitting light upon incidence of the ⁇ -rays. By this conversion, the scintillator element detects the ⁇ -rays.
  • the light emitted in the scintillator element is sufficiently diffused in the scintillator block 31 and input to the PMT 33 through the light guide 32.
  • the PMT 33 multiplies the light converted by the scintillator block 31 and converts it into an electric signal.
  • the electric signal is sent to the coincidence counting circuit 4 (see FIG. 1 ) as a pixel value.
  • the ⁇ -ray detector 3 is a DOI detector which is composed of scintillator elements arranged three-dimensionally and is composed of a plurality of layers arranged in the depth direction.
  • FIG. 2 illustrates a four-layer DOI detector, the number of layers is not particularly limited as long as it is plural.
  • the DOI detector is configured by laminating scintillator elements in the depth direction of radiation, and obtains the coordinate information in the depth direction (DOI: Depth of Interaction) and the lateral direction (direction in parallel to the incident surface) that caused the interaction by gravity center calculations.
  • DOI Depth of Interaction
  • the spatial resolution in the depth direction can be further improved by using the DOI detector. Therefore, the number of layers of the DOI detector is the number of layers of scintillator elements stacked along the depth direction.
  • FIG. 3 is a flowchart showing the processing steps and the flow of data of the attenuation coefficient image estimation method according to Example 1.
  • a subject is scanned by the PET apparatus 1 shown in FIG. 1 , and list mode data is acquired by the coincidence counting circuit 4 (see FIG. 1 ).
  • list mode data the energy information of the detected photon is recorded.
  • a standard energy window (e.g., 400 keV to 600 keV), that is, a reconstruction data energy window, and the measurement range and the bin width of the TOF measurement data in the TOF direction are set.
  • the bin means discretizing (dividing).
  • a pixel corresponds to a bin.
  • the TOF bin means a time division of the TOF information. For example, when the TOF bin is 100 [ps], the detection time difference is temporally separated with accuracy of 100 [ps].
  • the TOF-PET measurement data is generated according to the settings.
  • ⁇ ' be an image in which an non-uniform offset value is added to the quantitative attenuation coefficient image, and let ⁇ ' be a non-quantitative radioactivity image. Based on the optimization of the evaluation function regarding the measurement data, the image ⁇ ' and the radioactivity image ⁇ ' are calculated simultaneously. As described in the "Means for Solving the Problems" section, the image ⁇ ' also becomes an attenuation coefficient image, but is simply referred to as an "image ⁇ ' " in distinction from the quantitative attenuation coefficient image to be finally obtained.
  • the reconstruction algorithm in Step S1 is the simultaneous reconstruction algorithm in non-Patent Document 1.
  • Example 1 also in Examples 2 and 3 described later, the MLACF method described in non-Patent Document 1 is applied as the simultaneous reconstruction algorithm.
  • the specific method of the MLACF method please refer to non-Patent Document 1 mentioned above.
  • A' be an attenuation coefficient sinogram.
  • the radioactivity image ⁇ ' and the attenuation coefficient sinogram A' are estimated by the MLACF method.
  • the attenuation coefficient sinogram A' corresponds to the attenuation coefficient projection data in the present invention.
  • Step S2 ML-TR or ML-EM
  • the attenuation coefficient sinogram A' is reconstructed with a reconstruction algorithm (e.g., ML-TR method or ML-EM method) to generate a non-quantitative image ⁇ '.
  • a reconstruction algorithm e.g., ML-TR method or ML-EM method
  • the attenuation coefficient sinogram A' is log-transformed in advance.
  • Reference Document 1 Reference Document 1: Erdo an H, Fessler JA: Ordered subsets algorithms for transmission tomography. Phys Med Biol 44: 2835-2851, 1999 ).
  • Reference Document 2 Reference Document 2: L.A. Shepp and Y. Vardi. Maximum likelihood reconstruction for emission tomography. IEEE Trans. Med. Imaging, Vol. 1, pp. 113-122, 1982 ).
  • Steps S1 and S2 correspond to the reconstruction calculation step in the present invention.
  • the image ⁇ ' is binarization-processed by threshold processing. Then, a binarized image in which the subject region is "1" and the other regions are "0" is calculated as a subject mask image. Let m img be a subject mask image.
  • the line integral data (projection data) of the subject mask image m img is calculated (Projection). Then, by subjecting the projection data of the subject mask image m img to binarization processing by threshold processing, binarized data in which the projection line passing through the subject is "1" and the other projection lines are "0" is calculated as subject mask projection data. Let m proj be the subject mask projection data. Steps S3 and S4 correspond to the mask calculation step in the present invention.
  • ⁇ off be a non-uniform offset image.
  • the offset image ⁇ off is estimated by the reconstruction algorithm configured such that the forward projection data of the offset image ⁇ off is approximated to the subject mask projection data m proj . That is, the subject mask projection data m proj is converted into image data by the reconstruction algorithm (for example, the ML-EM method).
  • This image data is referred to as the offset image ⁇ off .
  • Step S5 corresponds to the offset estimation step in the present invention.
  • ⁇ be a region that can be approximated by a known attenuation coefficient value. At least one or more regions ⁇ are extracted using the image in which the subject region can be recognized calculated based on the measurement data (Extraction).
  • K( ⁇ 1) is the number of regions that can be approximated by a known attenuation coefficient value
  • ⁇ n is the n th region ⁇
  • respective regions ⁇ 1 , ..., ⁇ K are extracted at a region that can be approximated by air, a region that can be approximated by a brain tissue, and a region that can be approximated by a bone.
  • Step S6 corresponds to the reference region extraction step in the present invention.
  • S(X; ⁇ n ) be a statistic of the image X in the region ⁇ n or a value calculated from the statistics as a representative value
  • T(x 1 , x 2 , ..., x K ) be any statistic of K values x 1 , x 2 , ..., x K or a value calculated from statistics of K values x 1 , x 2 , ..., x K as a representative value
  • ⁇ n be the coefficient ⁇ in the region ⁇ n .
  • ⁇ is a coefficient.
  • the representative value is represented by, for example, a mean value, a median value, a trimmed mean value, a trimmed median value, or a weighted mean value of two or more of these values.
  • the "trimmed mean value” means a mean value of the remaining data from which extremely large/small values are removed.
  • the "trimmed median value” means a median value of the remaining data from which extremely large/small values are removed.
  • S( ⁇ '; ⁇ n ) is a representative value of the image ⁇ ' in the region ⁇ n
  • S( ⁇ off ; ⁇ n ) is a representative value of the offset image ⁇ ⁇ ff' in the region ⁇ n
  • Step S7 corresponds to the coefficient calculation step in the present invention.
  • ⁇ be the value (attenuation coefficient value) of an unknown true attenuation coefficient image.
  • Step S8 corresponds to the attenuation coefficient value correction step in the present invention.
  • the attenuation correction is performed using the attenuation coefficient image having the attenuation coefficient value ⁇ obtained in Step S8.
  • the transmittance of ⁇ -rays from the estimated attenuation coefficient image is obtained, and the transmittance is divided from the PET measurement data by converting it into the data from which the influence of the ⁇ -ray attenuation has been eliminated to perform the attenuation correction.
  • the estimated attenuation coefficient image is incorporated into the calculation formula of the image reconstruction to obtain a reconstructed image from which the influence of the attenuation of ⁇ -rays has been eliminated to perform the attenuation correction.
  • Step S1 and S2 based on the optimization of the evaluation function regarding the measurement data (measurement data of TOF-PET) of the positron CT in which the time-of-flight information of the annihilation radiation is included, an image ⁇ ' in which the non-uniform offset value is added to the quantitative attenuation coefficient image is calculated.
  • the radioactivity image ⁇ ' is calculated.
  • the reconstruction algorithm in Step S1 is the above-mentioned simultaneous reconstruction algorithm.
  • Steps S3 and S4 the subject mask data (that is, subject mask projection data m proj ) in the projection data space is calculated based on measurement data.
  • Step S5 the offset image ⁇ off is estimated by the reconstruction algorithm configured such that the forward projection data of the offset image ⁇ off is approximated to the subject mask projection data.
  • Step S6 at least one or more regions ⁇ are extracted using the image in which the subject region can be recognized calculated based on the measurement data.
  • the "image in which the subject region can be recognized calculated based on the measurement data” are, for example, an image ⁇ ' generated in Step S2, a radioactivity image ⁇ ' obtained in Step S1, a non-quantitative image estimated by the reconstruction algorithm (e.g., ML-EM method) different from the reconstruction algorithm (simultaneous reconstruction algorithm) in Step S1, and a subject mask image m img estimated from the above-mentioned subject mask projection data m proj .
  • the image is not limited to the illustrated images, and may be any image in which the subject region can be recognized calculated based on the measurement data.
  • extracting at least one or more regions ⁇ using an image in which a subject region is recognizable calculated based on the measurement data includes not only extracting the region ⁇ using a single piece of image information, but also extracting the region ⁇ using a combination of a plurality of pieces of image information (for example, logical sum or logical product).
  • Steps S7 and S8 are performed using the images ⁇ ' obtained in the above-described Steps S1 to S6, the offset image ⁇ off , and the region ⁇ .
  • Step S7 the coefficient ⁇ which reduces the error between the value of the image ⁇ ' in the region ⁇ and the known attenuation coefficient value is calculated.
  • Step S8 like the above-described formula (3), a value obtained by adding ⁇ off obtained by multiplying the offset image ⁇ off by the coefficient ⁇ to the value of the image ⁇ ' is corrected as an attenuation coefficient value ⁇ .
  • the attenuation coefficient value is corrected in Step S8 based on the mathematical relationship in which the difference between the value of the non-quantitative image ⁇ ' in the region ⁇ and the known attenuation coefficient value (the value of the true attenuation coefficient image) can be approximated by ⁇ off obtained by multiplying the offset image ⁇ off by the coefficient ⁇ (i.e., ⁇ ⁇ ⁇ '+ ⁇ off ). Therefore, in the attenuation coefficient image having the attenuation coefficient value ⁇ corrected in Step S8, a systematic error becomes small. As a result, a quantitative attenuation coefficient image can be generated, which enables an accurate attenuation correction of the radioactivity image.
  • Steps S1 and S2 corresponding to the above-mentioned reconstruction calculation step are performed by (b) a combination of a calculation algorithm in which an attenuation coefficient projection data is included as an unknown variable and an algorithm in which an image obtained by reconstructing the attenuation coefficient projection data is set as an image ⁇ '.
  • the algorithm (b) is a combination of the MLACF method described in non-Patent Document 1 which simultaneously estimates the non-quantitative radioactivity image ⁇ ' and the non-quantitative attenuation coefficient projection data (attenuation coefficient sinogram A' in each Example 1 to 3) and an algorithm in which the image obtained by reconstructing the attenuation coefficient projection data (attenuation coefficient sinogram A') is set as the image ⁇ '.
  • the algorithm in which the image obtained by reconstructing the attenuation coefficient projection data (attenuation coefficient sinogram A') is set as the image ⁇ ' in the above-described (b) is not specifically limited, and may be any algorithm as long as it is a reconstruction algorithm.
  • the attenuation coefficient sinogram A' is reconstructed by the ML-TR method or the ML-EM method to generate an image ⁇ '.
  • Step S3 and S4 corresponding to the above-mentioned mask calculation step are performed. That is, the mask calculation step is composed of a step of calculating a binarized image of the image ⁇ ' as a subject mask image m img (Step S3), a step of calculating projection data of a subject mask image m img ("projection" in the first half of Step S4), a step of calculating binarized data of the projection data of the subject mask image m img as subject mask projection data m proj ("Binarization Processing" in the second half of Step S4).
  • the image ⁇ ' is an attenuation coefficient image that is not quantitative, but, as in Examples 2 and 3 described later, even if images other than the attenuation coefficient image (for example, radioactivity image ⁇ ' or the radioactivity image ⁇ 2 ' in Example 3) and projection data are binarized, the subject mask projection data m proj can be calculated.
  • the reconstruction processing performed in Step S5 corresponding to the above-mentioned offset estimation step is performed by the statistical reconstruction calculation method represented by the ML-EM (Maximum Likelihood - Expectation Maximization) method or the like in this Example 1.
  • the reconstruction processing performed in Step S5 is not limited to the statistical reconstruction as in this Example 1. It may be performed by any calculation method of an analytical reconstruction, a statistical reconstruction, and an algebraic reconstruction.
  • an FBP Frtered Back Projection
  • the algebraic reconstruction for example, there is an ART (Algebraic Reconstruction Technique) method.
  • At least one or more of regions ⁇ extracted in Step S6 corresponding to the above-described reference region extraction step is a region of a tissue in which the attenuation coefficient is regarded as known.
  • the "region of a tissue in which the attenuation coefficient is regarded as known” is, for example, a region that can be approximated by water, a region that can be approximated by air, a region that can be approximated by a brain tissue, a region that can be approximated by a bone, a region that can be approximated by a lung tissue, a region that can be approximated by a soft tissue, etc.
  • the region is not limited to these exemplified tissues, but may be any tissues in which the approximation value of the attenuation coefficient can be known.
  • a brain tissue it is regarded as a region that can be approximated by water, so the attenuation coefficient value of water of 0.0096/mm can be used.
  • Step S7 corresponding to the above-mentioned coefficient calculation step is performed. That is, in Example 1, also in the Examples 2 to 4 described above, the coefficient ⁇ is calculated based on the representative value.
  • the representative value is represented by, for example, a mean value, a median value, a trimmed mean value, a trimmed median value, or a weighted mean value of two or more of these values. As described in the "Means for Solving the Problems" section, it is not limited to these exemplified values, but may be "a statistic or a value calculated from the statistic".
  • S( ⁇ '; ⁇ n ) is a representative value of the image ⁇ ' in the region ⁇ n
  • S( ⁇ off ; ⁇ n ) is a representative value of the offset image ⁇ off' in the region ⁇ n .
  • T( ⁇ 1 , ⁇ 2 , ..., ⁇ K ) is a representative value of the coefficient ⁇ 1 , ⁇ 2 , ..., ⁇ K .
  • the attenuation coefficient image estimation program 6 (see FIG. 1 ) according to this Example 1, by making the computer (in each Example, GPU, CPU, or the programmable device constituting the arithmetic circuit 5 shown in FIG. 1 ) execute the attenuation coefficient image estimation program according to Example 1, the attenuation coefficient value is corrected in Step S8 based on the mathematical relationship in which the difference between the value of the non-quantitative image ⁇ ' in the region ⁇ and the known attenuation coefficient value (the value of the true attenuation coefficient image) can be approximated by ⁇ off obtained by multiplying the offset image ⁇ off by the coefficient ⁇ .
  • the computing means in each Example, GPU, CPU, or the programmable device constituting the arithmetic circuit 5 shown in FIG. 1 in each Example
  • the computing means for executing the attenuation coefficient image estimation program 6 according to Example 1
  • the computing means for executing the attenuation coefficient image estimation program 6 according to Example 1
  • the attenuation coefficient is corrected.
  • FIG. 4 is a flowchart showing the processing steps and the flow of data of an attenuation coefficient image estimation method according to Example 2.
  • Example 1 the binarized image of the image ⁇ ' is calculated as a subject mask image m img , the projection data of the subject mask image m img is calculated, and the binarized data of the projection data of the subject mask image m img is calculated as subject mask projection data m proj .
  • the binarized data obtained by converting the measurement data of TOF-PET into a projection data format is calculated as subject mask projection data m proj .
  • Step S11 of FIG. 4 is the same as Step S1 of the above-described Example 1, and therefore the description thereof will be omitted.
  • Step S12 of FIG. 4 is the same as Step S2 of the above-described Example 1, and therefore the description thereof will be omitted.
  • Steps S11 and S12 correspond to the reconstruction calculation step in the present invention.
  • Step S3 and S4 of FIG. 3 are performed to calculate the subject mask image m img from the image ⁇ '.
  • Step S14 of FIG. 4 is performed to calculate a subject mask image m img from measurement data, instead of the image ⁇ '.
  • the measurement data is converted to a projection data format (Conversion).
  • binarized data in which the projection line passing through the subject is "1" and the other projection lines are "0" is calculated as subject mask projection data m proj .
  • Step S14 corresponds to the mask calculation step in the present invention.
  • Step S15 of FIG. 4 is the same as Step S5 of the above-described Example 1, and therefore the description thereof will be omitted.
  • Step S15 corresponds to the offset estimation step in the present invention.
  • Step S16 of FIG. 4 is the same as Step S6 of the above-described Example 1, and therefore the description thereof will be omitted.
  • Step S16 corresponds to the reference region extraction step in the present invention.
  • Step S17 of FIG. 4 is the same as Step S7 of the above-described Example 1, and therefore the description thereof will be omitted.
  • Step S17 corresponds to the coefficient calculation step in the present invention.
  • Step S18 of FIG. 4 is the same as Step S8 of the above-described Example 1, and therefore the description thereof will be omitted.
  • Step S18 corresponds to the attenuation coefficient value correction step in the present invention.
  • the attenuation coefficient value is corrected in Step S18 based on the mathematical relationship in which the difference between the value of the non-quantitative image ⁇ ' in the region ⁇ and the known attenuation coefficient value (the value of the true attenuation coefficient image) can be approximated by ⁇ off obtained by multiplying the offset image ⁇ off by the coefficient ⁇ . Therefore, in the attenuation coefficient image having the attenuation coefficient value ⁇ corrected in Step S18, the systematic error becomes small. As a result, a quantitative attenuation coefficient image can be generated, which enables an accurate attenuation correction of the radioactivity image.
  • Step S14 corresponding to the above-mentioned coefficient calculation step is performed. That is, the mask calculation step includes the step of calculating binarized data obtained by converting the measurement data of TOF-PET described above into the projection data format as subject mask projection data (Step S14).
  • the binarized data obtained by directly converting the measurement data of TOF-PET into a projection data format can be calculated as mask projection data m proj .
  • FIG. 5 is a flowchart showing the processing steps and the flow of data of an attenuation coefficient image estimation method according to Example 3 in the case of calculating subject mask projection data utilizing a radioactivity image estimated by the MLACF method.
  • FIG. 6 is a flowchart showing the processing steps and the flow of data of an attenuation coefficient image estimation method according to Example 3 in the case of calculating subject mask projection data utilizing a radioactivity image estimated by the reconstruction algorithm different from the MLACF method.
  • Example 1 the binarized image of the image ⁇ ' is calculated as a subject mask image m img , the projection data of the subject mask image m img is calculated, and the binarized data of the projection data of the subject mask image m img is calculated as subject mask projection data m proj . Further, in the above-described Example 2, the binarized data obtained by converting the measurement data of TOF-PET into a projection data format is calculated as subject mask projection data m proj .
  • the radioactivity image is calculated, the projection data of the radioactivity image is calculated, the binarized data of projection data (of radioactivity image) is calculated as subject mask projection data m proj .
  • Step S21 of FIG. 5 is the same as Step 1 of the above-described Example 1 and Step S11 of the above-described Example 2, and therefore the description thereof will be omitted.
  • Step S22 of FIG. 5 is the same as Step S2 of the above-described Example 1 and Step S12 of the above-described Example 2, and therefore the description thereof will be omitted. Steps S21 and S22 correspond to the reconstruction calculation step in the present invention.
  • Steps S3 and S4 of FIG. 3 are performed to calculate the subject mask image m img from the image ⁇ '. Further, in Example 2 described above, Step S14 of FIG. 4 is performed to calculate the subject mask image m img from the measurement data. In this Example 3, Step S24 of FIG. 5 is performed in order to calculate the subject mask image m img from the radioactivity image estimated based on the optimization of the evaluation function regarding measurement data instead of the image ⁇ ' of Example 1 and the measurement data of Example 2.
  • the line integral data (projection data) of the radioactivity image ⁇ ' estimated based on the optimization of the evaluation function regarding the measurement data in the MLACF method is calculated (Projection). That is, in FIG. 5 , the projection data of the radioactivity image ⁇ ' may be calculated utilizing the radioactivity image ⁇ ' estimated by the MLACF method of Step S21. Then, by subjecting the projection data of the radioactivity image ⁇ ' to binarization processing by threshold processing, binarized data in which the projection line passing through the subject is "1" and the other projection lines are "0" is calculated as subject mask projection data m proj .
  • Step S24 corresponds to the mask calculation step in the present invention.
  • Step S25 of FIG. 5 is the same as Step S1 of the above-described Example 1 and Step S15 of the above-described Example 2, and therefore the description thereof will be omitted.
  • Step S25 corresponds to the offset estimation step in the present invention.
  • Step S26 of FIG. 5 is the same as Step S6 of the above-described Example 1 and Step S16 of the above-described Example 2, and therefore the description thereof will be omitted.
  • Step S26 corresponds to the reference region extraction step in the present invention.
  • Step S27 of FIG. 5 is the same as Step S7 of the above-described Example 1 and Step S17 of the above-described Example 2, and therefore the description thereof will be omitted.
  • Step S27 corresponds to the coefficient calculation step in the present invention.
  • Step S28 of FIG. 5 is the same as Step S8 of the above-described Example 1 and Step S18 of the above-described Example 2, and therefore the description thereof will be omitted.
  • Step S28 corresponds to the attenuation coefficient value correction step in the present invention.
  • Step S31 of FIG. 6 is the same as Step S21 of FIG. 5 , and therefore the description thereof will be omitted.
  • Step S32 of FIG. 6 is the same as Step S22 of FIG. 5 , and therefore the description thereof will be omitted. Steps S31 and S32 correspond to the reconstruction calculation step in the present invention.
  • Step S24 shown in FIG. 5 is performed to calculate subject mask projection data m proj utilizing radioactivity image ⁇ ' estimated by the MLACF method.
  • Step S33 and S34 of FIG. 6 are performed in order to calculate subject mask projection data m proj utilizing a radioactivity image estimated by a reconstruction algorithm different from the MLACF method.
  • a radioactivity image is estimated based on the optimization of the evaluation function regarding the measurement data in the reconstruction algorithm (for example, the ML-EM method) different from the MLACF method.
  • the radioactivity image estimated by the reconstruction algorithm different from the MLACF method is set as ⁇ 2 ' in distinction from the radioactivity image ⁇ ' estimated by the MLACF method.
  • the line integral data (projection data) of the radioactivity image ⁇ 2 ' estimated based on the optimization of the evaluation function regarding the measurement data in the reconstruction algorithm different from the MLACF method is calculated (Projection). Then, by subjecting the projection data of the radioactivity image ⁇ 2 ' to binarization processing by the threshold processing, binarized data in which the projection line passing through the subject is "1" and the other projection lines are "0" is calculated as subject mask projection data m proj . Steps S33 and S34 correspond to the mask calculation step in the present invention.
  • Step S35 of FIG. 6 is the same as Step S25 of FIG. 5 , and therefore the description thereof will be omitted. Step S35 corresponds to the offset estimation step in the present invention.
  • Step S36 of FIG. 6 is the same as Step S26 of FIG. 5 , and therefore the description thereof will be omitted.
  • Step S36 corresponds to the reference region extraction step in the present invention.
  • Step S37 of FIG. 6 is the same as Step S27 of FIG. 5 , and therefore the description thereof will be omitted.
  • Step S37 corresponds to the coefficient calculation step in the present invention.
  • Step S38 of FIG. 6 is the same as Step S28 of FIG. 5 , and therefore the description thereof will be omitted.
  • Step S38 corresponds to the attenuation coefficient value correction step in the present invention.
  • the attenuation coefficient value is corrected in Step S28 of FIG. 5 and the attenuation coefficient value in Step S38 of FIG. 6 based on the mathematical relationship in which the difference between the value of the non-quantitative image ⁇ ' and the known attenuation coefficient value (the value of the true attenuation coefficient image) in the region ⁇ can be approximated by ⁇ off obtained by multiplying the offset image ⁇ off by the coefficient ⁇ . Therefore, in the attenuation coefficient image having the attenuation coefficient value ⁇ corrected in Step S28 of FIG. 5 or Step S38 of FIG. 6 , the systematic error becomes small. As a result, a quantitative attenuation coefficient image can be generated, which enables an accurate attenuation correction of the radioactivity image.
  • Step S24 of FIG. 5 corresponding to the above-mentioned coefficient calculation step or Steps S33 and S34 of FIG. 6 are performed. That is, the mask calculation step includes a step of calculating the radioactivity image ( ⁇ ' in FIG. 5 and ⁇ 2 ' in FIG. 6 ) based on the optimization of the evaluation function regarding the measurement data of the TOF-PET (described above) (Step S21 in FIG. 5 and Step S33 in FIG. 6 ), a step of calculating projection data of a radioactivity image ( ⁇ ' in FIG. 5 and ⁇ 2 ' in FIG. 6 ) ("Projection" in the first half of Step S24 in FIG. 5 ; "Projection" in the first half of Step S34 in FIG.
  • the reconstruction algorithm for calculating the radioactivity image is not particularly limited.
  • subject mask projection data m proj can be calculated utilizing the above-mentioned radioactivity image ⁇ ' estimated by the simultaneous reconstruction algorithm.
  • the subject mask projection data m proj may be calculated utilizing the radioactivity image ⁇ 2 ' estimated by a reconstruction algorithm (for example, the ML-EM method) different from the above-mentioned simultaneous reconstruction algorithm (MLACF method or MLAA method).
  • a reconstruction algorithm for example, the ML-EM method
  • MAACF method simultaneous reconstruction algorithm
  • FIG. 7 is a flowchart showing the processing steps and the flow of data of an attenuation coefficient image estimation method according to Example 4.
  • the above-mentioned reconstruction calculation step is performed by the combination of the MLACF method and an algorithm in which the image obtained by reconstructing the attenuation coefficient projection data (in each of Examples 1 to 3, attenuation coefficient sinogram A') is set as the image ⁇ '.
  • Step S1 Step S11 in Example 2 and Step S21 or S31 in Example 3 in which the radioactivity image ⁇ ' and the attenuation coefficient sinogram A' are estimated by the MLACF method
  • Step S2 Step S12 in Example 2, Steps S22 or S32 in Example 3 in which an image obtained by reconstructing the attenuation coefficient sinogram A' is set to the image ⁇ ' is performed.
  • the radioactivity image ⁇ ' and the image ⁇ ' are simultaneously calculated by the MLAA method.
  • Steps S1 and S2 (Steps S11 and S12 in Example 2, Steps S21 and S22 or S31 and S32 in Example 3) using the MLACF method are integrated into one Step S41 when the MLAA method is used in this Example 4.
  • Reference Document 3 Reference Document 3: A Rezaei (K.U. Leuven), M. Defrise, G. Bal et. al., "Simultaneous reconstruction of activity and attenuation in time-of-flight PET", IEEE Trans. Med. Imag., 31 (12), 2224-2233, 2012 ).
  • Steps S41 corresponds to the reconstruction calculation step in the present invention.
  • Step S43 of FIG. 7 is the same as Step S3 of the above-described Example 1, and therefore the description thereof will be omitted.
  • Step S44 of FIG. 7 is the same as Step S4 of the above-described Example 1, and therefore the description thereof will be omitted. Steps S43 and S44 correspond to the mask calculation step in the present invention.
  • Step S45 of FIG. 7 is the same as Step S5 of the above-described Example 1, Step S15 of the above-described Example 2, and Step of the above-described Example 3 (Step S25 in FIG. 5 , Step S35 in FIG. 6 ), and therefore the description thereof will be omitted.
  • Step S45 corresponds to the offset estimation step in the present invention.
  • Step S46 of FIG. 7 is the same as Step S6 of the above-described Example 1, Step S16 of the above-described Example 2, and Step of the above-described Example 3 (Step S26 in FIG. 5 , Step S36 in FIG. 6 ), and therefore the description thereof will be omitted.
  • Step S46 corresponds to the reference region extraction step in the present invention.
  • Step S47 of FIG. 7 is the same as Step S7 of the above-described Example 1, Step S17 of the above-described Example 2, and Step of the above-described Example 3 (Step S27 in FIG. 5 , Step S37 in FIG. 6 ), and therefore the description thereof will be omitted.
  • Step S47 corresponds to the coefficient calculation step in the present invention.
  • Step S48 of FIG. 7 is the same as Step S8 of the above-described Example 1, Step S18 of the above-described Example 2, and Step of the above-described Example 3 (Step S28 in FIG. 5 , Step S38 in FIG. 6 ), and therefore the description thereof will be omitted.
  • Step S48 corresponds to the attenuation coefficient value correction step in the present invention.
  • FIG. 7 is a flowchart of Example 4 when applied in cases where Steps S1 and S2 in FIG. 3 of Example 1 described above are integrated into Step S43.
  • Example 4 may be applied in cases where Steps S11 and S12 in FIG. 4 of Example 2 described above are integrated into Step S43, and Example 4 may be applied in cases where Steps S21 and S22 in FIG. 5 of Example 3 described above or Steps S31 and S32 in FIG. 6 are integrated.
  • the attenuation coefficient value is corrected in Step S48 based on the mathematical relationship in which the difference between the value of the non-quantitative image ⁇ ' in the region ⁇ and the known attenuation coefficient value (the value of the true attenuation coefficient image) can be approximated by ⁇ off obtained by multiplying the offset image ⁇ off by the coefficient ⁇ . Therefore, in the attenuation coefficient image having the attenuation coefficient value ⁇ corrected in Step S48, a systematic error becomes small. As a result, a quantitative attenuation coefficient image can be generated, which enables an accurate attenuation correction of the radioactivity image.
  • Step S41 corresponding to the above-mentioned reconstruction calculation step may be performed by (a) a calculation algorithm in which the image ⁇ ' is included as an unknown variable.
  • the algorithm (a) is an MLAA method that simultaneously reconstructs the non-quantitative radioactivity image ⁇ ' and the image ⁇ ' (non-quantitative attenuation coefficient image).
  • FIG. 8 is a flowchart showing the processing steps and the flow of data of an attenuation coefficient image estimation method according to Example 5.
  • the coefficient ⁇ is calculated based on the representative value.
  • the coefficient ⁇ is calculated based on the error evaluation function.
  • Step S51 of FIG. 8 is the same as Step S1 of the above-described Example 1, Step S11 of the above-described Example 2, and Step of the above-described Example 3 (Step S21 in FIG. 5 , Step S31 in FIG. 6 ), and therefore the description thereof will be omitted.
  • Step S52 of FIG. 8 is the same as Step S2 of the above-described Example 1, Step S12 of the above-described Example 2, and Step of the above-described Example 3 (Step S22 in FIG. 5 , Step S32 in FIG. 6 ), and therefore the description thereof will be omitted.
  • Steps S51 and S52 correspond to the reconstruction calculation step in the present invention.
  • Step S53 of FIG. 8 is the same as Step S3 of the above-described Example 1 and Step S43 of the above-described Example 4, and therefore the description thereof will be omitted.
  • Step S54 of FIG. 8 is the same as Step S4 of the above-described Example 1 and Step S44 of the above-described Example 4, and therefore the description thereof will be omitted. Steps S53 and S54 correspond to the mask calculation step in the present invention.
  • Step S55 of FIG. 8 is the same as Step S5 of the above-described Example 1, Step S15 of the above-described Example 2, Step of the above-described Example 3 (Step S25 in FIG. 5 , Step S35 in FIG. 6 ), and Step S45 of the above-described Example 4, and therefore the description thereof will be omitted.
  • Step S55 corresponds to the offset estimation step in the present invention.
  • Step S56 of FIG. 8 is the same as Step S6 of the above-described Example 1, Step S16 of the above-described Example 2, Step of the above-described Example 3 (Step S26 in FIG. 5 , Step S36 in FIG. 6 ), and Step S46 of the above-described Example 4, and therefore the description thereof will be omitted.
  • Step S56 corresponds to the reference region extraction step in the present invention.
  • the coefficient ⁇ is calculated based on the representative value.
  • the coefficient ⁇ is calculated based on the error evaluation function.
  • ⁇ known be an image in which a known attenuation coefficient is set in the known attenuation coefficient in the region ⁇
  • D ⁇ (X, Y) be an error evaluation function of the image X and the image Y in the region ⁇ .
  • the error evaluation function D ⁇ (X, Y) as exemplified in the difference sum D ⁇ (X, Y) ⁇ n ⁇
  • of the absolute value is not particularly limited.
  • Step S57 corresponds to the coefficient calculation step in the present invention.
  • Step S48 of FIG. 8 is the same as Step S8 of the above-described Example 1, Step S18 of the above-described Example 2, Step of the above-described Example 3 (Step S28 in FIG. 5 , Step S38 in FIG. 6 ), and Step S48 of the above-described Example 4, and therefore the description thereof will be omitted.
  • Step S58 corresponds to the attenuation coefficient value correction step in the present invention.
  • FIG. 8 is a flowchart of Example 5 applied when the calculation of coefficient ⁇ based on the representative value according to Step S7 in FIG. 3 of Example 1 described above is replaced with the calculation of coefficient ⁇ based on the error evaluation function according to Step S57.
  • Example 5 may be applied.
  • Example 5 may be applied.
  • Example 5 may be applied.
  • Example 5 may be applied.
  • the attenuation coefficient value is corrected in Step S58 based on the mathematical relationship in which the difference between the value of the non-quantitative image ⁇ ' in the region ⁇ and the known attenuation coefficient value (the value of the true attenuation coefficient image) can be approximated by ⁇ off obtained by multiplying the offset image ⁇ off by the coefficient ⁇ . Therefore, in the attenuation coefficient image having the attenuation coefficient value ⁇ corrected in Step S58, a systematic error becomes small. As a result, a quantitative attenuation coefficient image can be generated, which enables an accurate attenuation correction of the radioactivity image.
  • the coefficient ⁇ is calculated based on the error evaluation function.
  • K( ⁇ 1) be a region that can be approximated by a known attenuation coefficient value
  • ⁇ n be the n th region ⁇
  • D ⁇ n (X, Y) be an error evaluation function of an image X and an image Y within the region ⁇ n
  • w n (n 1, ..., K) be a coefficient range from 0 to 1.
  • the function f( ⁇ ) in which the coefficient ⁇ is represented by weighted sum of D ⁇ 1 ( ⁇ 1 known , ⁇ ' + ⁇ off ),... , D ⁇ K ( ⁇ K known , ⁇ ' + ⁇ ⁇ ff ) by the coefficient w 1 ,..., w K for each region ⁇ 1 , ..., ⁇ K , n 1, ... , K. That is, when generalized, the function f( ⁇ ) is expressed by the following formula (5).
  • the present invention is suitable for estimation of an attenuation coefficient image using measurement data measured by a TOF measurement type PET apparatus.

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EP17912063.9A 2017-05-29 2017-05-29 Procédé d'estimation d'image de coefficient d'absorption, programme d'estimation d'image de coefficient d'absorption et dispositif de tomographie par positrons équipé de ce dernier Withdrawn EP3633411A4 (fr)

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CN110691992A (zh) 2020-01-14
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US20200085397A1 (en) 2020-03-19
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